Discussion Forum

Hello all,

I am currently setting up a COMSOL workflow which solves for two items:

The first is a stationary study to solve for a parameter known as the surface potential via the Poisson-Boltzmann equation (Mott-Shottky case).

The output of the stationary study is the surface potential parameter (Φ), which then uses the following approximation to calculate the diffusion coefficient at each depth value.

D(x) = Doexp(-2eΦ(x)/(kT)) where Do, e, k, and T are all known. In the stationary study, the Φ(x) is assigned to the dependent variable 'u'.

This Φ parameter is spatially variant, and therefore, the diffusion coefficient is likewise spatially (or rather depth) variant as described in the above equation. I have successfully solved for the diffusion coefficient as a function of depth in my system, but the current challenge is to then implement these diffusion values in a subsequent time-dependent study to solve (2) Fick's second law.

In my time-dependent study for Fick's second law, I am using the 'Coefficient Form PDE' and in the diffusion coefficient input, I re-enter the expression Doexp(-2eu/(kT)). However, it doesn't seem like the diffusion coefficient in the time-dependent study is properly accounting for the spatial variance as determined from the stationary study. Does annyone have any insight, reccomendations or suggestions on why this might be the case and what to do to resolve such an issue?

Many thanks for your time!